Finite Group Databasebeta

← #14914517

Subgroups — #14914517

Order 2816.

2238 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623219C211yesmaximal, characteristic
2#13071671C212yesmaximal, complemented
3#13071671C212yesmaximal, complemented
4#13071624C212yesmaximal
5#13071618C212yesmaximal
6#13071578C212yesmaximal, complemented
7#13071535C212yesmaximal, complemented
8#13071475C212yesmaximal
9#13071471C212yesmaximal
10#13071422C211yesmaximal, characteristic, complemented
11#13071420C211yesmaximal, characteristic, complemented
12#13071417C211yesmaximal, characteristic, complemented
13#13071265C212yesmaximal, complemented
14#13071150C212yesmaximal
15C4×#66949C212yesmaximal
16#13071013C211yesmaximal, characteristic
17#13070980C212yesmaximal, complemented
18C4×C4⋊C4×D11C211yesmaximal, characteristic
19C11×#2336C211yesmaximal, characteristic, complemented
20C2×C11×#125C2211yescharacteristic
21#10623219C4116yescomplemented
22C2×#66949C2212yes—
23C2×#66949C2212yes—
24C2×#66945C2211yescharacteristic
25C2×#66945C2211yescharacteristic
26C2×C4⋊C4×D11C2212yes—
27C2×#66941C2211yescharacteristic
28C2×#66941C2211yescharacteristic
29C2×#66940C2212yes—
30C2×#66940C2212yes—
31C2×#66940C2212yes—
32C2×#66940C2212yes—
33C2×C42×D11C2211yescharacteristic
34C2×C42×D11C2211yescharacteristic
35C2×C42×D11C2211yescharacteristic
36C2×#66923C2211yescharacteristic
37C2×C4×Dic22C2212yes—
38C2×C4×Dic22C2212yes—
39C11×#389C2212yes—
40C11×#387C2212yes—
41C11×#387C2212yes—
42C11×#387C2212yes—
43C11×#387C2212yes—
44C11×#383C2211yescharacteristic
45C4×C11×C4⋊C4C2212yes—
46C4×C11×C4⋊C4C2211yescharacteristic
47#10622602C2212yes—
48#10622602C2212yes—
49#10622598C2212yes—
50#10622594C2212yes—
51#10622594C2212yes—
52#10622594C2212yes—
53#10622594C2212yes—
54#10622591C2212yes—
55#10622590C2212yes—
56C4⋊C4×Dic11C2212yes—
57C4⋊C4×Dic11C2212yes—
58C4⋊C4×Dic11C2212yes—
59#10622585C2212yes—
60#10622585C2212yes—
61#10622585C2212yes—
62C4×(C2×D11)⋊C4C2212yes—
63C4×(C2×D11)⋊C4C2212yes—
64#10622550C2211yescharacteristic
65C4×C4⋊Dic11C2211yescharacteristic
66#10622546C2212yes—
67#10622545C2212yes—
68C4×Dic11⋊C4C2212yes—
69C4×Dic11⋊C4C2212yes—
70C4×Dic11⋊C4C2212yes—
71C4×Dic11⋊C4C2211yescharacteristic
72C4×Dic11⋊C4C2211yescharacteristic
73C4×Dic11⋊C4C2212yes—
74#10622281C2212yes—
75#10622281C2212yes—
76#10622280C2212yes—
77#10622279C2211yescharacteristic
78#10622279C2212yes—
79#10622279C2211yescharacteristic
80#10622279C2212yes—
81#10622277C2212yes—
82D11×#95C2212yes—
83#10622268C2212yes—
84#10622267C2212yes—
85#10622267C2212yes—
86#10622266C2212yes—
87#10622266C2212yes—
88#10622265C2212yes—
89#10622264C2212yes—
90#10622264C2212yes—
91#10622263C2212yes—
92#10622263C2211yescharacteristic
93#10622263C2211yescharacteristic
94#10622262C2212yes—
95#10622262C2212yes—
96#10622262C2212yes—
97#10622262C2212yes—
98#10622262C2212yes—
99#10622261C2212yes—
100#10622261C2212yes—
101#10622260C2212yes—
102#10622260C2212yes—
103#10622260C2212yes—
104#10622259C2212yes—
105#10622259C2212yes—
106#10622259C2212yes—
107#10622259C2212yes—
108C22×C4×D11C2312yes—
109C22×C4×D11C2312yes—
110C22×C4×D11C2311yescharacteristic
111C22×C4×D11C2311yescharacteristic
112C22×C4×D11C2311yescharacteristic
113C22×Dic22C2312yes—
114C22×Dic22C2312yes—
115C11×#125C2×C418yescomplemented
116C2×C11×C4⋊C4C2312yes—
117C2×C11×C4⋊C4C2312yes—
118C2×C11×C4⋊C4C2312yes—
119C2×C11×C4⋊C4C2312yes—
120C2×C11×C4⋊C4C2312yes—
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C42×C11C2312yes—
124C2×C42×C11C2312yes—
125C2×C42×C11C2311yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C42×C11C2311yescharacteristic
128C2×(C2×D11)⋊C4C2312yes—
129C2×(C2×D11)⋊C4C2312yes—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×C4⋊Dic11C2312yes—
133C2×C4⋊Dic11C2312yes—
134C2×C4⋊Dic11C2312yes—
135C2×C4⋊Dic11C2311yescharacteristic
136C2×C4⋊Dic11C2311yescharacteristic
137C2×Dic11⋊C4C2312yes—
138C2×Dic11⋊C4C2312yes—
139C2×Dic11⋊C4C2312yes—
140C2×Dic11⋊C4C2312yes—
141C2×Dic11⋊C4C2312yes—
142C2×Dic11⋊C4C2312yes—
143C2×Dic11⋊C4C2312yes—
144C2×Dic11⋊C4C2312yes—
145C2×Dic11⋊C4C2312yes—
146C2×Dic11⋊C4C2312yes—
147C2×Dic11⋊C4C2312yes—
148C2×Dic11⋊C4C2312yes—
149C2×C4×Dic11C2312yes—
150C2×C4×Dic11C2312yes—
151C2×C4×Dic11C2312yes—
152C2×C4×Dic11C2312yes—
153C2×C4×Dic11C2312yes—
154C2×C4×Dic11C2312yes—
155C2×C4×Dic11C2312yes—
156C2×C4×Dic11C2312yes—
157C2×C4×Dic11C2311yescharacteristic
158C2×C4×Dic11C2311yescharacteristic
159C2×C4×Dic11C2312yes—
160C2×C4×Dic11C2312yes—
161C2×C4×Dic11C2311yescharacteristic
162C2×C4×Dic11C2311yescharacteristic
163C2×C4×Dic11C2311yescharacteristic
164C2×C4×Dic11C2312yes—
165C2×C4×Dic11C2312yes—
166#66949C2×C4116yes—
167#66949C2×C4116yes—
168#66945C2×C418yes—
169#66945C2×C418yes—
170C4⋊C4×D11—28no—
171#66941C2×C418yescomplemented
172#66941C2×C418yescomplemented
173#66940—28no—
174#66940—44no—
175#66940C2×C4116yescomplemented
176#66940C2×C4116yescomplemented
177C42×D11—42no—
178C42×D11—42no—
179C42×D11C2×C418yes—
180#66923C2×C418yescomplemented
181C4×Dic22—28no—
182C4×Dic22—44no—
183C11×#95C2312yes—
184C11×#95C2312yes—
185C11×#95C2312yes—
186C11×#95C2312yes—
187C11×#95C2311yescharacteristic
188C11×#95C2312yes—
189C11×#95C2312yes—
190C11×#95C2312yes—
191C11×#95C2311yescharacteristic
192C11⋊#95C2312yes—
193C11⋊#95C2312yes—
194C11⋊#95C2312yes—
195C11⋊#95C2312yes—
196C11⋊#95C2312yes—
197C11⋊#95C2312yes—
198C11⋊#95C2312yes—
199C11⋊#95C2312yes—
200C11⋊#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2312yes—
203C11⋊#95C2312yes—
204C11⋊#95C2312yes—
205C11⋊#95C2312yes—
206C11⋊#95C2312yes—
207C11⋊#95C2312yes—
208C11⋊#95C2312yes—
209C11⋊#95C2312yes—
210C11⋊#95C2312yes—
211C11⋊#95C2311yescharacteristic
212C11⋊#95C2311yescharacteristic
213#34235—111nomaximal, Sylow
214C23×D11C2411yescharacteristic
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2411yescharacteristic
219C22×C4×C11C2411yescharacteristic
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2411yescharacteristic
223C22×C4×C11C2412yes—
224C22×Dic11C2412yes—
225C22×Dic11C2412yes—
226C22×Dic11C2412yes—
227C22×Dic11C2411yescharacteristic
228C22×Dic11C2412yes—
229C22×Dic11C2412yes—
230C22×Dic11C2412yes—
231C22×Dic11C2411yescharacteristic
232C22×Dic11C2411yescharacteristic
233C2×C4×D11—24no—
234C2×C4×D11—22no—
235C2×C4×D11—22no—
236C2×C4×D11—24no—
237C2×C4×D11—24no—
238C2×C4×D11—24no—
239C2×C4×D11—24no—
240C2×C4×D11—24no—
241C2×C4×D11—42no—
242C2×C4×D11—42no—
243C2×C4×D11C22×C414yes—
244C2×C4×D11C22×C414yes—
245C2×C4×D11C22×C414yes—
246C2×Dic22—24no—
247C2×Dic22—24no—
248C2×Dic22—24no—
249C2×Dic22—24no—
250C2×Dic22C22×C418yes—
251C2×Dic22C22×C418yes—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—24no—
254C11×C4⋊C4—42no—
255C11×C4⋊C4C22×C418yes—
256C11×C4⋊C4C22×C418yes—
257C11×C4⋊C4C22×C414yes—
258C11×C4⋊C4C22×C414yes—
259C42×C11—24no—
260C42×C11—42no—
261C42×C11—41no—
262C42×C11—41no—
263C42×C11C22×C414yes—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4C22×C418yes—
267(C2×D11)⋊C4C22×C418yes—
268C4⋊Dic11—24no—
269C4⋊Dic11—24no—
270C4⋊Dic11—42no—
271C4⋊Dic11C22×C414yes—
272C4⋊Dic11C22×C414yes—
273Dic11⋊C4—24no—
274Dic11⋊C4—24no—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4—42no—
279Dic11⋊C4—42no—
280Dic11⋊C4C22×C418yes—
281Dic11⋊C4C22×C418yes—
282Dic11⋊C4C22×C418yes—
283Dic11⋊C4C22×C418yes—
284Dic11⋊C4#4118yes—
285C4×Dic11—24no—
286C4×Dic11—24no—
287C4×Dic11—24no—
288C4×Dic11—24no—
289C4×Dic11—24no—
290C4×Dic11—24no—
291C4×Dic11—24no—
292C4×Dic11—42no—
293C4×Dic11—41no—
294C4×Dic11—41no—
295C4×Dic11—42no—
296C4×Dic11—42no—
297C4×Dic11C22×C414yes—
298C4×Dic11C22×C414yes—
299C4×Dic11C22×C414yes—
300C4×Dic11C22×C418yes—
301C4×Dic11C22×C418yes—
302C2×#533—111no—
303#2365—112no—
304#2365—112no—
305#2360—112no—
306#2360—112no—
307#2356—112no—
308#2351—112no—
309#2343—112no—
310#2343—112no—
311#2336—111no—
312#2336—111no—
313#2336—111no—
314#2336D1111yescharacteristic, complemented
315#2320—112no—
316C4×C22⋊Q8—112no—
317C4×C22⋊Q8—112no—
318#2283—111no—
319#2276—112no—
320C2×C4×C4⋊C4—111no—
321C23×C11C2511yescharacteristic
322C22×D11—22no—
323C22×D11—21no—
324C22×D11—21no—
325C22×D11C23×C412yes—
326C22×D112−1+414yes—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—21no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—21no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11C23×C412yes—
347C2×C4×C11C23×C412yes—
348C2×C4×C11C23×C414yes—
349C2×C4×C11C23×C414yes—
350C2×C4×C11C23×C412yes—
351C2×C4×C11C2×#4114yes—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11C23×C412yes—
369C2×Dic11C23×C414yes—
370C2×Dic11C23×C414yes—
371C2×Dic11C23×C412yes—
372C2×Dic11C23×C412yes—
373C2×Dic11C2×#4114yes—
374C2×Dic11C2×#4114yes—
375C2×Dic11H(5,𝔽2)12yes—
376C2×Dic112−1+412yes—
377C4×D11—28no—
378C4×D11—28no—
379C4×D11—28no—
380C4×D11—48no—
381C4×D11—48no—
382Dic22—216no—
383Dic22—216no—
384#533—1116no—
385C2×C4⋊Q8—111no—
386C2×C4⋊Q8—111no—
387C2×#125—111no—
388C2×#125C2×D1111yescharacteristic
389C2×C22⋊Q8—112no—
390C2×C22⋊Q8—112no—
391C2×C4×Q8—112no—
392C2×C4×Q8—112no—
393C2×C4×Q8—112no—
394C2×C4×Q8—112no—
395C2×C4×Q8—112no—
396C2×C4×Q8—112no—
397C2×#117—111no—
398C2×#117—111no—
399C22×C4⋊C4—112no—
400C22×C42—111no—
401C22×C42—111no—
402C22×C42—111no—
403#391—112no—
404#391—112no—
405#391—112no—
406#391—112no—
407#389—112no—
408#389—112no—
409#389—112no—
410#389—112no—
411#389—112no—
412#389—112no—
413#389—112no—
414#389C2×D1112yes—
415#387—112no—
416#387—112no—
417#387—112no—
418#387—112no—
419#387—112no—
420#387—112no—
421#387—112no—
422#387—112no—
423#387—112no—
424#387—112no—
425#387—112no—
426#387—112no—
427#387C2×D1112yes—
428#387C2×D1112yes—
429#387C2×D1112yes—
430#387C2×D1112yes—
431#385—112no—
432#385—112no—
433#385—112no—
434#385—112no—
435#383—111no—
436#383—112no—
437#383—112no—
438#383C2×D1111yescharacteristic
439#382—112no—
440#382—112no—
441#382—111no—
442#382—111no—
443#381—112no—
444#380—112no—
445C4×C4⋊C4—112no—
446C4×C4⋊C4—112no—
447C4×C4⋊C4—112no—
448C4×C4⋊C4—111no—
449C4×C4⋊C4—111no—
450C4×C4⋊C4—112no—
451C4×C4⋊C4—112no—
452C4×C4⋊C4—112no—
453C4×C4⋊C4—112no—
454C4×C4⋊C4—111no—
455C4×C4⋊C4—112no—
456C4×C4⋊C4—112no—
457C4×C4⋊C4—112no—
458C4×C4⋊C4—112no—
459C4×C4⋊C4—112no—
460C4×C4⋊C4C2×D1111yescharacteristic
461C4×C4⋊C4C2×D1112yes—
462C4×C22⋊C4—112no—
463C4×C22⋊C4—112no—
464C4×C22⋊C4—112no—
465C4×C22⋊C4—112no—
466C4×C22⋊C4—111no—
467C4×C22⋊C4—111no—
468#376—112no—
469#376—112no—
470#376—112no—
471C2×#95—112no—
472C22×C11C24×C411yescharacteristic
473C22×C11C22×#4112yes—
474C22×C11C2×H(5,𝔽2)11yescharacteristic
475C22×C11C2×2−1+412yes—
476C22×C11C2×2−1+411yescharacteristic
477C2×D11—22no—
478C2×D11—22no—
479C2×D11—24no—
480C2×D11—24no—
481C2×D11#51914yes—
482C4×C11—24no—
483C4×C11—22no—
484C4×C11—22no—
485C4×C11—24no—
486C4×C11—22no—
487C4×C11—24no—
488C4×C11—42no—
489C4×C11—42no—
490C4×C11—42no—
491Dic11—24no—
492Dic11—22no—
493Dic11—24no—
494Dic11—24no—
495Dic11—42no—
496Dic11—42no—
497Dic11—42no—
498Dic11C4×#4114yes—
499Dic11#52014yes—
500C22×Q8—112no—
501C22×Q8—112no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—111no—
505C23×C4—112no—
506C23×C4—112no—
507C4⋊Q8—118no—
508C4⋊Q8—118no—
509#125—118no—
510#125C4×D1118yescomplemented
511C22⋊Q8—1116no—
512C22⋊Q8—1116no—
513C4×Q8—1116no—
514C4×Q8—1116no—
515C4×Q8—228no—
516C4×Q8—228no—
517C4×Q8—444no—
518C4×Q8—444no—
519#117—118no—
520#117—118no—
521C2×C4⋊C4—112no—
522C2×C4⋊C4—111no—
523C2×C4⋊C4—111no—
524C2×C4⋊C4—112no—
525C2×C4⋊C4—112no—
526C2×C4⋊C4—112no—
527C2×C4⋊C4—112no—
528C2×C4⋊C4—112no—
529C2×C4⋊C4—112no—
530C2×C4⋊C4—112no—
531C2×C4⋊C4—112no—
532C2×C4⋊C4—112no—
533C2×C4⋊C4—112no—
534C2×C4⋊C4—112no—
535C2×C4⋊C4—112no—
536C2×C4⋊C4—112no—
537C2×C4⋊C4—112no—
538C2×C4⋊C4—228no—
539C2×C4⋊C4C22×D1112yes—
540C2×C4⋊C4C22×D1112yes—
541C2×C4⋊C4C22×D1112yes—
542C2×C4⋊C4C22×D1111yescharacteristic
543C2×C4⋊C4C22×D1111yescharacteristic
544C2×C4⋊C4C22×D1112yes—
545C2×C4⋊C4C22×D1112yes—
546C2×C22⋊C4—112no—
547C2×C22⋊C4—112no—
548C2×C22⋊C4—112no—
549C2×C22⋊C4—112no—
550C2×C42—112no—
551C2×C42—112no—
552C2×C42—111no—
553C2×C42—111no—
554C2×C42—111no—
555C2×C42—118no—
556C2×C42—112no—
557C2×C42—112no—
558C2×C42—112no—
559C2×C42—112no—
560C2×C42—112no—
561C2×C42—112no—
562C2×C42—112no—
563C2×C42—112no—
564C2×C42—112no—
565C2×C42—112no—
566C2×C42—111no—
567C2×C42—111no—
568C2×C42—442no—
569C2×C42—442no—
570C2×C42C22×D1112yes—
571C2×C42C22×D1112yes—
572C2×C42C22×D1111yescharacteristic
573C2×C42C22×D1111yescharacteristic
574C2×C42C22×D1111yescharacteristic
575#95—112no—
576#95—112no—
577#95—112no—
578#95—112no—
579#95—112no—
580#95—112no—
581#95—112no—
582#95—112no—
583#95—112no—
584#95—111no—
585#95—111no—
586#95—112no—
587#95—112no—
588#95—112no—
589#95—112no—
590#95—112no—
591#95—112no—
592#95—112no—
593#95—112no—
594#95—112no—
595#95—112no—
596#95C22×D1112yes—
597#95C22×D1112yes—
598#95C22×D1112yes—
599#95C22×D1111yescharacteristic
600#95C22×D1111yescharacteristic
601#95C22×D1112yes—
602#95C22×D1112yes—
603#95C22×D1112yes—
604#95C22×D1112yes—
605C2×C11C2×C4×#4111yescharacteristic
606C2×C11C2×#51911yescharacteristic
607C2×C11C2×#52011yescharacteristic
608C2×C11#352012yes—
609C2×C11#352312yes—
610D11—24no—
611C24—111no—
612C2×Q8—118no—
613C2×Q8—118no—
614C2×Q8—224no—
615C2×Q8—224no—
616C2×Q8—224no—
617C2×Q8—224no—
618C22×C4—111no—
619C22×C4—111no—
620C22×C4—111no—
621C22×C4—112no—
622C22×C4—112no—
623C22×C4—112no—
624C22×C4—114no—
625C22×C4—114no—
626C22×C4—114no—
627C22×C4—112no—
628C22×C4—112no—
629C22×C4—112no—
630C22×C4—222no—
631C22×C4—224no—
632C22×C4—222no—
633C22×C4—224no—
634C22×C4—224no—
635C22×C4—224no—
636C22×C4—224no—
637C22×C4—224no—
638C22×C4—442no—
639C22×C4—442no—
640C22×C4C23×D1112yes—
641C22×C4C23×D1112yes—
642C22×C4C23×D1112yes—
643C22×C4C23×D1111yescharacteristic
644C22×C4C23×D1111yescharacteristic
645C22×C4C23×D1112yes—
646C22×C4C23×D1112yes—
647C22×C4C23×D1111yescharacteristic
648C22×C4C23×D1112yes—
649C4⋊C4—24no—
650C4⋊C4—24no—
651C4⋊C4—42no—
652C4⋊C4—114no—
653C4⋊C4—114no—
654C4⋊C4—118no—
655C4⋊C4—118no—
656C4⋊C4—118no—
657C4⋊C4—118no—
658C4⋊C4—118no—
659C4⋊C4—224no—
660C4⋊C4—224no—
661C4⋊C4—224no—
662C4⋊C4—224no—
663C4⋊C4—224no—
664C4⋊C4—224no—
665C4⋊C4—224no—
666C4⋊C4—442no—
667C4⋊C4—442no—
668C4⋊C4—442no—
669C4⋊C4C2×C4×D1114yes—
670C4⋊C4C2×C4×D1114yes—
671C4⋊C4C2×C4×D1118yes—
672C4⋊C4C2×C4×D1118yes—
673C22⋊C4—118no—
674C22⋊C4—118no—
675C22⋊C4—224no—
676C22⋊C4—224no—
677C42—24no—
678C42—41no—
679C42—41no—
680C42—42no—
681C42—114no—
682C42—114no—
683C42—114no—
684C42—118no—
685C42—118no—
686C42—224no—
687C42—224no—
688C42—224no—
689C42—224no—
690C42—224no—
691C42—224no—
692C42—224no—
693C42—441no—
694C42—441no—
695C42—442no—
696C42—442no—
697C42—442no—
698C42C2×C4×D1114yes—
699C11#3423511yescharacteristic, complemented, Sylow
700C23—112no—
701C23—114no—
702C23—222no—
703C23—221no—
704C23—221no—
705C23C24×D1111yescharacteristic
706Q8—2216no—
707Q8—2216no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—21no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—112no—
728C2×C4—112no—
729C2×C4—114no—
730C2×C4—112no—
731C2×C4—112no—
732C2×C4—112no—
733C2×C4—114no—
734C2×C4—114no—
735C2×C4—114no—
736C2×C4—228no—
737C2×C4—228no—
738C2×C4—228no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—222no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—448no—
756C2×C4—448no—
757C2×C4C22×C4×D1112yes—
758C2×C4C22×C4×D1112yes—
759C2×C4C22×C4×D1112yes—
760C2×C4C22×C4×D1114yes—
761C2×C4C22×C4×D1114yes—
762C2×C4#41×D1114yes—
763C22—114no—
764C22—224no—
765C22—224no—
766C22—222no—
767C22—222no—
768C22C23×C4×D1111yescharacteristic
769C22C2×#41×D1112yes—
770C22D11×H(5,𝔽2)11yescharacteristic
771C22D11×2−1+412yes—
772C22D11×2−1+411yescharacteristic
773C4—24no—
774C4—22no—
775C4—24no—
776C4—22no—
777C4—22no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—114no—
783C4—114no—
784C4—224no—
785C4—224no—
786C4—222no—
787C4—224no—
788C4—442no—
789C4—442no—
790C4—442no—
791C2—224no—
792C2C4×#41×D1111yescharacteristic
793C2D11×#51911yescharacteristic
794C2D11×#52011yescharacteristic
795C2#1308265712yes—
796C2#1308270812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2336C2
socle, cosocleC23×C11C25
prime radicalC23×D11C24
hypercenter#2336D11
hypocenterC11#34235
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2336

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #13071671C2semidirect
3. #13071671C2semidirect
6. #13071578C2semidirect
7. #13071535C2semidirect
10. #13071422C2semidirect
11. #13071420C2semidirect
12. #13071417C2semidirect
13. #13071265C2semidirect
17. #13070980C2semidirect
19. C11×#2336C2semidirect
21. #10623219C4semidirect
115. C11×#125C2×C4semidirect
171. #66941C2×C4semidirect
172. #66941C2×C4semidirect
175. #66940C2×C4semidirect
176. #66940C2×C4semidirect
180. #66923C2×C4semidirect
314. #2336D11semidirect
510. #125C4×D11semidirect
699. C11#34235semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106232192
#130716712
#130716242
#130716182
#130715782
#130715352
#130714752
#130714712
#130714222
#130714202
#130714172
#130712652
#130711502
C4×#669492
#130710132
#130709802
C4×C4⋊C4×D112
C11×#23362
#3423511